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How was the size of Earth first measured? (2015)

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Re: How was the size of Earth first measured? (2015)

#71

Post by Hayvok »

nico wrote: post #42
082349872349872 wrote: post #27

Earlier quoted context omitted.

Wow, TIL the reason Aristarchus' contemporaries didn't accept his heliocentric model...

pages 156-158: “Ironically, when Aristarchus proposed the heliocentric model, his contemporaries dismissed it, on the grounds that they did not observe any parallax effects...” “ so the heliocentric model would have implied that the stars were an absurdly large distance away.” “[Which, of course, they are.]”

I’m not familiar with the Ancient Greek objections here, but I remember Renaissance scientists being hung up on this same thing.

They had measured the visible diameter of stars and without any parallax, would’ve also meant that the stars were absurdly large in addition to far away.

I don’t think they had a problem with the distance, per se, but the implied size.

(You have to treat stars as points - any perceived diameter is an illusion - but nobody knew that at the time.)

Re: How was the size of Earth first measured? (2015)

#72

Post by jiggawatts »

njarboe wrote: post #39
pomian wrote: post #16

Earlier quoted context omitted.

Staking claims, where corner posts were placed at half kilometer intervals, were usually paced on foot, estimating for canyons, stream crossings, and other diversions. Some claims were continuous up to 20km by 20 km. This was in complete wilderness, in the Yukon, British Columbia and so on. Pre GPS. Not that long ago! They used topographic maps for reference. It is amazing how accurate the claims were, when transferr…

Imagine what it took to make the highly accurate topo maps they relied on.

https://en.wikipedia.org/wiki/Great_Trigonometrical_Survey

Re: How was the size of Earth first measured? (2015)

#73

Post by mcmoor »

nico wrote: post #42
082349872349872 wrote: post #27

Earlier quoted context omitted.

Wow, TIL the reason Aristarchus' contemporaries didn't accept his heliocentric model...

pages 156-158: “Ironically, when Aristarchus proposed the heliocentric model, his contemporaries dismissed it, on the grounds that they did not observe any parallax effects...” “ so the heliocentric model would have implied that the stars were an absurdly large distance away.” “[Which, of course, they are.]”

Knowing this makes me perplexed whenever someone treats geocentrists as idiots. Sometimes science really can get only as far as our "eyes" can see.

Re: How was the size of Earth first measured? (2015)

#74

Post by drpixie »

fwungy wrote: post #70

What is the sun was smaller and closer than we think? One could sew the same result in that instance.

Unless the sun was VERY close, the actual distance doesn't matter. What matters is that the sun (or a star, or whatever you use as a reference) is so far away that there is no practical difference between "far away" and "even further".

For practical purposes, we treat the sun as being an infinite distance away, and the error caused by it being ONLY 93,000,000 miles away is much smaller than Eratosthenes could measure :)

It's similar to drawing perspectives, you draw perspective lines to join at the distant horizon. You don't care how far to the distance horizon.

(Those ancient Greeks had amazing understanding of geometry. Much better than most of us.)

Re: How was the size of Earth first measured? (2015)

#75

Post by oxygen_crisis »

divbzero wrote: post #59

5% error is incredible. I wonder what Eratosthenes thought of his own measurement. Did he believe it was accurate? Or questioned if unknown factors could have thrown off his calculation?

He measured it in "stadia" and there was no consensus about exactly how long a stadion was. The definitions ranged widely, from ~150m to ~210m.

The low error assessment comes from magnanimously (but baselessly) choosing to use the definition of a stadion which assigns Eratosthenes the lowest error.

https://en.wikipedia.org/wiki/Stadion_(unit)

Re: How was the size of Earth first measured? (2015)

#76

Post by StackOverlord »

ahazred8ta wrote: post #49
YeBanKo wrote: post #44

Earlier quoted context omitted.

Why are Pyramids the first evidence of Earth’s measurements?

There are crackpots who think the builders of the Great Pyramid knew the size of the Earth. https://www.hallofmaat.com/numerology/a-critique-of-graham-h...

You can get to the absolute dimensions of the pyramid from the crackpot equations though:

https://pasteboard.co/cIMzn8KktEZy.png

https://tobeornottobe.org/the-great-pyramid-intro/math-const...

https://pastebin.com/TsUtcWAa

I just found a great recap on this topic that also fits nicely with the points your link brings up, shedding a better light on the number 43,200 in other cultures (the scaling factor between the pyramid and the earth dimensions for those who TL;DR).

https://fossana.medium.com/the-pyramids-of-giza-have-propert...

It also addresses the fact the speed of light in m/s is encoded three times in the pyramid, twice in the dimensions, in cubits and meters, and another times via the GPS coordinates (yes 3 fucking times !). But how would they know about the duration of a second ? I don't know ! What I know is that 43,200 * 2 = 84,600, the number of seconds in a day.

The thing goes deeper with this man and his investigations of the first edition of Shakespeare's Sonnets.

https://www.youtube.com/watch?v=0xOGeZt71sg

https://www.youtube.com/watch?v=nIS-hNrr0-c

Re: How was the size of Earth first measured? (2015)

#77

Post by andrewprock »

The podcast Song of Urania does a super deep dive into the history of astronomy, including this specific measurement. One of the insights the podcast brings to light is that there were many such estimates; relative size of the Earth, Moon and Sun - distance to the Moon, etc. By reviewing the distribution of these estimates, and the methods applied, the host of the podcast suggest that Eratosthenes was lucky to get quite so close.

https://songofurania.com/

Re: How was the size of Earth first measured? (2015)

#78

Post by andrewprock »

willis936 wrote: post #25

"First" is awfully confident assertion about an event thousands of years ago. "Earliest known" is more accurate.

If you study the context and development of Greek culture, astronomy, and mathematics, a good case can be made that if it wasn't Eratosthenes, it was another Greek astronomer.

Re: How was the size of Earth first measured? (2015)

#79

Post by alehlopeh »

drpixie wrote: post #74
fwungy wrote: post #70

What is the sun was smaller and closer than we think? One could sew the same result in that instance.

Unless the sun was VERY close, the actual distance doesn't matter. What matters is that the sun (or a star, or whatever you use as a reference) is so far away that there is no practical difference between "far away" and "even further". For practical purposes, we treat the sun as being an infinite distance away, and the error caused by it being ONLY 93,000,000 miles away is much smaller than Eratosthenes could measure…

Good answer but weirdly judgy last sentence. More like, a handful of ancient Greeks had a better understanding of geometry than most of us, just like a handful of us has a better understanding of geometry than most of us. And of course, a handful of us has a better understanding of geometry than most ancient Greeks.

Re: How was the size of Earth first measured? (2015)

#80

Post by labster »

bryan0 wrote: post #11

Terrence Tao has an old excellent presentation on the “cosmic ladder” which shows how from this measurement you can build up to measure the largest distances in the visible universe: https://terrytao.files.wordpress.com/2010/10/cosmic-distance...

The thing that stood out to me was the second rung of the ladder, the Moon. Having a large companion satellite is not a prerequisite for life (probably), so how would aliens without one bridge this gap? It seems like it would take a lot more physical theory beyond simple geometry to get there.
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